In intelligent tutoring systems (ITS), the representation of subject matter knowledge is referred to as a domain model. A domain model is an integral part of an ITS, and typically is strongly connected with both the model of the student's knowledge (student model) and the model of how to teach the subject matter (pedagogical/expert model).
There are several different formulations of domain models in use today, with representations ranging from logic to statistics. Conceptual graphs, also referred to as concept maps, have been used as declarative ITS domain models in a middle ground between first order logic and statistical representations. In general, a concept map comprises a set of nodes (concepts) and edges (relations) describing a core concept or answering a core question.
One example is CIRCSIM-Tutor, a dialogue-based tutor for causal relationships in the cardiovascular system. The goal of CIRCSIM-Tutor is for the student to learn an underlying causal concept map and use it to solve problems and construct explanations. Causal relations have a +/− valence, indicating a direct or inverse relationship of one concept/variable on another. For example, carrots may be directly causally related (+) to rabbits, such that an increase in the number of carrots leads to an increase in the number of rabbits. At least one version of CIRCSIM-Tutor used an overlay model of a concept map as a student model, and the concept map is also used for understanding student utterances. This multiple functionality demonstrates that concept maps can be flexible representations.
Another ITS that uses concept maps as a domain model is Betty's Brain, which uses the “learning by teaching” paradigm to help student learn about relationships in river ecosystems. Students teach an agent, Betty, whose brain is reified as a causal concept map highly similar to that of CIRCSIM-Tutor, with additional hierarchical (i.e. is-a) and descriptive relations (i.e. has-property). Students use an available hypertext as a source for information, and then “teach” specific nodes and relations in that domain by populating them with content and linking them together. Once created, the concept map can be queried by the student, or even allow Betty to “take” a quiz, using a qualitative reasoning algorithm. The student-created concept map is complemented by a hidden expert-created concept map. This map is used by a mentor agent, Mr. Davis, to provide hints and feedback. Thus, one way to characterize the goal of the system is to bring the student's map into alignment with the expert map. As exemplified by CIRCSIM-Tutor and Betty's Brain, conceptual graphs can be used as both domain models and overlay student models, as well as to interpret student utterances, generate explanations, and perform qualitative reasoning. However, in both CIRCSIM-Tutor and Betty's Brain, expert conceptual graphs need to be authored.
There are different approaches taken towards conceptual graphs based upon different subject matters and fields. In one formulation (now an ISO standard), conceptual graphs are interchangeable with predicate calculus and thus equivalent in power to logical/inferential domain models. Of particular importance is grain size, i.e., the level of granularity given to nodes and relationships. In these conceptual graphs, grain size is very small, such that each argument (e.g., John) is connected to other arguments (e.g., Mary) through an arbitrary predicate (e.g., John loves Mary). Aside from the tight correspondence to logic, grain size turns out to be a relevant differentiator amongst conceptualizations of conceptual graphs amongst different fields.
Another formulation comes from the psychology literature, with some emphasis on modeling question asking and answering. In this formulation of conceptual graphs, nodes themselves can be propositions (e.g., “a girl wants to play with a doll”), and relations are limited as much as possible to a generic set of propositions for a given domain. For example, one such categorization consists of 21 relations including is-a, has-property, has-consequence, reason, implies, outcome, and means. A particular advantage of limiting relations to these categories is that the categories can then be set into correspondence with certain question types (e.g., definitional, causal consequent, procedural) for both answering questions and generating them.
Finally, concept maps are widely used in science education for both enhancing student learning and assessment. Even in this community, there are several formulations of concept maps, including hierarchical maps, cluster maps, MindMaps, computer-generated associative networks, and concept-circle diagrams, among others. One example is the SemNet formulation, which is characterized by a central concept (which has been determined as highly relevant in the domain) linked to other concepts using a relatively prescribed set of relations. End nodes can be arbitrary, and cannot themselves be linked to unless they are another core concept in the domain. Interestingly, in the field of biology, 50% of all links are is-a, part-of, or has property, which suggests that generic relations may be able to account for a large percentage of links in any domain, with only some customization to be performed for specific domains. An example SemNet triple (i.e., start node/relation/end node) is “prophase includes process chromosomes become visible.” Several thousand of such triples are available online, illustrating the viability of this representational scheme for biology.
However, the creation and development of a domain model is very challenging and time-consuming, and often requires special authoring tools to accomplish. Accordingly, there is a desire to keep domain models as simple as possible to ease authoring, while keeping them as complex as effectively possible to maximize learning.